Question

a sequence of transformations is described below.

• a translation
• a dilation about a point ( p )
• another translation
• a rotation about the point ( p )

which of the following must be preserved under this sequence of transformations?
choose 1 answer:
a angle measures only
b segment lengths only
c both angle measures and segment lengths
d neither angle measures nor segment lengths

Explanation:

1. Analyze each transformation:

• Translation: Preserves both angle measures and segment lengths (isometry).
• Dilation: Changes segment lengths (scales them) but preserves angle measures (since it's a similarity transformation).
• Rotation: Preserves both angle measures and segment lengths (isometry).

1. Overall effect: Since dilation is included, segment lengths are not preserved (they are scaled), but angle measures are preserved through all transformations (translation, dilation, rotation all preserve angle measures—dilation preserves angles, translations and rotations are isometries that also preserve angles). So only angle measures are preserved.

Answer:

A. Angle measures only